Thick walled pressure vessel

ABSTRACT

A thick walled pressure vessel having a tubular wall is prestressed by bending to resist extreme external pressures, the bending being applied by the external pressure being resisted. The tubular or cylindrical wall contains internal axial cuts which divide the wall into axial sectors with faying surfaces therebetween so that the application of external pressure decreases the curvature of the sectors to prestress them.

United States Patent 1191 Donohue 1 Oct. 2, 1973 l l THICK WALLEDPRESSURE VESSEL [75] Inventor: John Donohue, Howell, NY.

[73] Assignec: Struthers Scientific and International Corporation, NewYork, NY.

221 Filed: Oct. 13, 1970 21 Appl. No.: 80,511

Related US. Application Data [62] Division of Ser. No. 691,090, Nov.22,1967,

[56] References Cited UNITED STATES PATENTS 2,133,058 10/1938 Paine29/477 X 3,075,484 1/1963 Benteler... 29/477 X 3,093,103 6/1963Bcrkelcy.. 29/4773 3,269,424 8/1966 Fisher 1 29/446 3,314,141 4/1967Bacroix 29/477.7 X

Primary Examiner-Henry T. Klinksick A!t0rneyWilliam A. Drucker [57]ABSTRACT A thick walled pressure vessel having a tubular wall isprestressed by bending to resist extreme external pressures, the bendingbeing applied by the external pressure being resisted. The tubular orcylindrical wall contains internal axial cuts which divide the wall intoaxial sectors with faying surfaces therebetween so that the applicationof external pressure decreases the curvature of the sectors to prestressthem.

4 Claims, 9 Drawing Figures PATENTED 3.762.448

sum 10F 3 P FIG]. 1

Compresrslbn Tens/on PATENTEUBBT 2W 3.762.448

SHEET 2 BF 3 Compress/gr) Tens/0n 1 THICK WALLED PRESSURE VESSEL CROSSREFERENCES TO RELATED APPLICATIONS This application is a division ofpatent application Ser. No. 691,090 filed Nov. 22, I967, now abandoned.

BACKGROUND OF THE INVENTION It is well known that when a normallyunstressed thick-walled cylinder is subjected to high pressure on eitherthe outside or the inside, the circumferential stress at the inside ofthe wall is greater than that at the outside by the amount of thepressure applied. It is, therefore, common in producing such cylindersthat are to be subject to a pressure that is a significant fraction ofthe allowable stress, to trap into the wall a beneficial prestress whichwill be more or less cancel out the difference in stress between theoutside and inside and thereby allow a higher average stress. This hasbeen done by shrinking one or more cylinders together, winding with wireor tape under tension, applying controlled pressure so that a portionofthe wall is stressed beyond its yield point, and by controlled quenchingfrom the metals plastic temperature. This disclosure describes a novelmethod of using bending to produce the desired results, and points outthat its use has advantages not only in internally pressurized vessels,but even more particularlyin externally pressurized vessels, where thefirst two methods cannot be used and the third is often impractical.

SUMMARY OFTHE INVENTION With regard to external pressure, where thedesired prestress is circumferential tension at the inner wall andcompression at the outer, with a consequent radial tension in the wall,winding is obviously impractical and concentric cylinders will haveinitial clearance, making them highly susceptible to buckling. With thebending method, however, all final stresses are compressive; and it canbe shown that, by suitably calculating the planes of the fayingsurfaces, the prestresses can be applied simultaneously with thepressure. In fact, the paradoxical but sound conclusion can be reachedthat a vessel, lightly but suitably sealed, composed of twosemi-cylindrical halves, can be stronger than a continuous cylindricalvessel of the same dimensions.

BRIEF DESCRIPTION OF THE DRAWING FIGS. 1 and 2 are diagrams showing theinternal and external radii of a thick walled pressure vessel withradial, circumferential, and axial stresses graphed as a function ofcylinder wall thickness;

FIGS. 3, 4, 6 and 9 are end views of two sectors of a cylinder havinginternal faying surfaces so that the cylinder will be-prestressed bybending as it is subjected to external pressure, FIGS. 3, 4, 6 and Pshowing the effect of progressively increasing external pressure on thecylinder; and

FIGS. 5, 7 and 8 show stress and pressure forces acting on a half ofeach of the sectors of FIGS. 4, 6 and 9 respectively.

DESCRIPTION OF THE PREFERRED EMBODIMENTS To evaluate the desiredprestress in a thick walled cylinder subjected to outside or insidepressure, a choice must be made from several theories of tube failure:maximum stress, strain energy, maximum shear, etc. In the ease of theclosed tubular vessel under external pressure only, there are no tensilestresses involved. Failure must occur at the inner surface as this isthe only free surface. Also, since the stresses involved are compressionin both axial and circumferential directions, and failure by directcompression is inconceivable, failure must be by shear. For the mostefficient condition, the shear stress should be equal in all directions,or the axial and the circumferential compression at the inner surfaceshould be equal, giving a resultant shearing stress equal to one-halfthe compressive stress and at 45 to any radius.

The formulae for stresses in a thick cylinder are Internal PressureExternal Pressure where s, circumferential stress s, radial stress s,axial stress for the case of a vessel closed at the ends p pressure rradius and subscripts i and 0 denote inside" and outside, respectively.Pressure and compressive stress are considered positive and tensilestress negative.

Further ll ll II and, in particular,

where,

s radial stress due to bending s circumferential stress due to bending Dan arbitrary constant For the case of external pressure on a vessel withclosed ends, we will set up a prestress x, by bending such that Theequations above for bending stresses in a curved beam may be solved forD and the compensating stresses which may be obtained by bending may becalculated. As shown in FIG. 1, a section through a cylinder has beendrawn with an internal radius r, and an external radius r so that r/r;=2. Superimposed on the horizontal radius Tof the cylinder is a graphwith a horizontal axis OT and a positive vertical axis OP and a negativevertical axis O-P.

In FIG. 1, line 20 is a graph of the uncompensated circumferentialstress in terms of a given outside pressure p plotted on axis OP againstcylinder wall thickness plotted on axis OT. Line 24 is a similar graphof the circumferential prestress set up in the cylinder wall by bendingto decrease its curvature. Line 21 is a graph of the combinedcircumferential stresses which result in the cylinder when prestressedby bending and subjected to an outside pressure p,,. Line 21 indicatesthat a cylinder prestressed by bending may have an insidecircumferential stress of about one half that of an unprestressedcylinder. While the outside stress of a prestressed cylinder is shown tobe almost 2.5p,,, there is no place for the metal to flow. It is to benoted that even axial flow will be resisted by the axial stressindicated by the graph line 26.

Line 23 is a graph of the radial prestress produced by bending. Line 22is a graph of the radial stress produced by an external pressure of pLine 25 is a graph of the combined radial stresses in a prestressedcylinder subjected to an external pressure p,,. It is interesting tonote that the radial stress produced by bending and neglected by theWinkler theory is of benefit in reducing the radial stress near r, is aprestressed cylinder. This reduction of radial stress reduces thetendency for shear failure by radially inward flow.

If, however, it is desired to maintain a constant compressive stressacross the tube wall, as called for by the maximum stress theory offailure, such a stress would be This again may be solved for D and thestresses calculated.

FIG. 2 shows a cylinder and a graph similar to that shown in FIG. 1.Line 20 again graphs the circumferential stress resulting from anoutside pressure p,,. Line 27 graphs the circumferential stress in thecylinder resulting from bending so that the combined circumferentialstresses in the cylinder will be approximately constant through itsthickness when subjected to an external pressure p Line 28 is a graph ofthe combined circumferential stresses in the cylinder which may thus beprestressed to approximate a constant compressive stress across its wallwhen subjected to an external pressure To analyze longitudinal joints ina cylinder under hydrostatic external pressure, let us consider such acylinder of indefinite length with prestress due only to bending. Thestress pattern will be the same over any radial section because thebending moment across any such section is constant and independent ofthe central angle. The external pressure is constant, directed towardthe center, and independent of the central angle. There is, therefore,no shear on any radial plane. Under full design pressure, there will beonly compression on such a radial plane.

Therefore, if it is imagined making a diametral cut while maintainingthe external pressure, there will be no change in shape or stressdistribution, since such a change would have to be due to tension(separation of cut surfaces), shear (sliding of one cut surface on theother), or a change of shape of the mating surfaces without separation,which could only be caused by isolated irregularities in the stresspattern. While such may exist, they will be equally superimposed on thestressed and unstressed state and may, for this discussion, beneglected. With release of the external pressure, the two halves willseparate along the cut, and the prestress due to bending will bereleased so that the halves will be free of stress. As the prestress wasproduced by a bending moment tending to open up the halves to 1r radiansor the halves in the unstressed position will have a slightly greaterangular measure, say 71' E.

Since the angle at which I make the diametral cut makes no difference, asecond diametral cut at an angle to the first should have not moreeffect, except that on release of pressure I will have four unstressedsectors. Any adjacent pair will then have a total angular measure of wE. Also, when unstressed, adjacent pairs must fit tightly together,because any separation would indicate a stressed condition before thecut, contrary to the original hypothesis. The plane cuts originally madeunder pressure, therefore, remain plane in the released condition, andconversely.

FIGS. 3-9 show two sectors or halves 61 and 62 of a cylindrical shell 60joined at 63. The outer wall of each sector curves 5 percent more than180 as shown in the Drawing. This would be in the order of 0.5 percentfor a steel shell 60. FIG. 3 shows the shell 60 with no externalpressure on it. FIG. 6 shows the effect of sufficient external pressureto reduce the excess angle E to one-half the original.

FIG. 5 shows the stresses and forces on on half the upper section. Thedownward component of the pressure p is resisted by an upward force F=prmore or less concentrated at the outer corner 63. While the horizontalcomponent of the pressure plus the excess moment of the vertical forceM=Fr is resisted by an unsymmetrical pattern of stresses across thevertical cross section which range from a fairly high compression at theoutside to a low tension on the inside. In FIG. 6, the external pressurehas increased to a value sufficient to close the mating surfacescompletely. At this external pressure, the stress at the inside radiusis zero around the circumference. Since there is zero stress, there mustbe zero strain, and the inside circumference is the same as in theunstressed state. However, as the total angular measure has decreased 5percent, the inside radius has increased 5 percent. Now, neglectingradial strains, which are slight, the wall thickness has not changed.Therefore, while the outer radius has increased by the same amount, ithas only increased by three-fourths as great a percent. Thus, since thedecrease in angular measurement is the same throughout, there is ashortening or compressive strain of the outer circumference of 1%percent. FIG. 7 shows the stress and pressure pattern for thiscondition. It can be shown that the outer stress will be equal to themaximum design pressure and that the pressure to produce this stresswill be (r r )/2r,, times this design pressure.

FIG. 9 shows the cylinder 60 under the maximum design pressure which hasproduced a uniform maximum design stress across the wall in accordancewith the formulae hereinbefore given. It should be noted that betweenFIGS. 6 and 9, r, has been compressed to its original value, causing acircumferential strain of 5 percent. r has also returned to its originalvalue, causing an additional strain of 3% percent which, added to thestrain already present in FIG. 7 makes the external strain equal to theinternal.

Thus, it may be seen that longitudinal sectors of a pressure vesseljoined only at their outer points of contact to provide a seal may beable to resist greater external pressures than a solid cylindricalpressure vessel of the same wall thickness. If desired, the fayingsurfaces of the sectors of such a pressure vessel may be forced togetherby suitable bending and then welded to prestress the vessel to resistgreater external pressures. However, in most applications such as deepdiving marine exploration devices, the bending and the prestress may beapplied by the external pressure which is to be resisted.

While it is possible to apply the concepts of this invention to aspherical pressure vessel by making cuts in a thick walled sphere todivide the sphere into sectors with bases corresponding to regularpolygons, the cuts would be made while the sphere was subjected topressure. On release of the pressure, the sectors, being concave cones,could not fit perfectly tightly without distortion.

However, solid unprestressed spherical ends may be used on a cylindricalvessel with the same inside and outside radii as the stresses in theunprestressed ends of a spherical ended cylindrical vessel willgenerally be well under the stresses in the prestressed cylindricalportion. While this invention has been applied to cylindrical pressurevessels, it could equally well be applied to vessels with oval or otheraxial enclosing walls.

I claim:

1. In a thick walled pressure vessel, a tubular wall for resisting highexternal pressure, said wall containing internal axial cuts dividing thewall into axial sectors with faying surfaces therebetween, the fayingsurfaces being sealed at their outer edges at the outer surface of saidwall, said sectors elastically bending to decrease their curvature underexternal pressure to prestress said sectors and thereby said wall ofsaid pressure vessel.

2. The combination according to claim 1 wherein said faying surfaces areclosed under external pressure.

3. The combination according to claim 1 wherein said tubular wall iscylindrical, and wherein said axial sectors when unprestressed havecurvatures totalling more than 360 and are elastically bent by externalpressure to close said faying surfaces and have curvatures thentotalling substantially 360.

4. In the process of forming a thick walled pressure vessel having acurved metal closing wall of an integral layer of material wherein theclosing wall has axial sectors joined and sealed at their outer edges;

abutting the metal closing wall axial sectors leaving open fayingsurfaces therebetween,

and bending the closing wall to decrease its curvature to resist higherexternal pressures by applying ecternal pressure to close the fayingsurfaces.

UNETED STATES PATENT OFFECE CERTEFICA TE 0F CQEQTEQN Patent 3,762.):8Dated October 2, 1973 Inventofls) John Donohue Howell It is certifiedthat error appears in the above-identified patent and that said LettersPatent ere hereby corrected as shown below:

On the cover sheet item [75] "John Donohue, Howell, N Y.

should read John Donohlie Howell, New City, N.Y.

Signed and sealed this 26th day of February 19714..

(SEAL) Attest:

EDWAPD M.FLETCHER,JR.

Attesting Officer MARSHALL NN Commissioner of Patents FORM PO-IOSO(10-69) uscoMM-Dc scan-poo tr [1.5. GOVERNMENT PRINTING OFFICE I)0-866-3JLI56

1. In a thick walled pressure vessel, a tubular wall for resisting highexternal pressure, said wall containing internal axial cuts dividing thewall into axial sectors with faying surfaces therebetween, the fayingsurfaces being sealed at their outer edges at the outer surface of saidwall, said sectors elastically bending to decrease their curvature underexternal pressure to prestress said sectors and thereby said wall ofsaid pressure vessel.
 2. The combination according to claim 1 whereinsaid faying surfaces are closed under external pressure.
 3. Thecombination according to claim 1 wherein said tubular wall iscylindrical, and wherein said axial sectors when unprestressed havecurvatures totalling more than 360* and are elastically bent by externalpressure to close said faying surfaces and have curvatures thentotalling substantially 360*.
 4. In the process of forming a thickwalled pressure vessel having a curved metal closing wall of an integrallayer of material wherein the closing wall has axial sectors joined andsealed at their outer edges; abutting the metal closing wall axialsectors leaving open faying surfaces therebetween, and bending theclosing wall to decrease its curvature to resist higher externalpressures by applying ecternal pressure to close the faying surfaces.